The log left the cliff with a horizontal velocity of 7.5 m/s. When it reached the water, it had a vertical velocity of -8.9 m/s. What was the log's speed (two dimensional) before it entered the water

v = 11.6 m/s

Explanation:

Assuming no other forces acting upon the log than gravity (which acts only in the vertical direction)  in the horizontal direction, velocity must be constant at any point.So, before it entered the water, its velocity has two components, as follows:vₓ = 7.5 m/svy = -8.9 m/sWe can find the magnitude of the velocity vector, just applying Pythagorean Theorem to both components, as follows:

       

       ⇒ v = 11.6 m/s